Icosian Game

The Icosian Game is a game devised by William Hamilton and
first described by him in 1857 at a meeting of the British Association in
Dublin. The object of the game is to find a way around the edges of a dodecahedron
so that every vertex (corner) is visited once and only once. A path such
as this became known as a Hamilton
circuit, though the task of finding a circuit that passes just once
through every vertex of a shape seems to have arisen first in connection
with Leonhard Euler's study of the knight's
tour. Two years before Hamilton introduced his game, Thomas Kirkman posed the problem explicitly in a paper that he submitted to the Royal Society:
Given a graph of a polyhedron,
does there exist a cycle passing through every vertex?

The Icosian Game stemmed from Hamilton's invention of a curious kind of
algebra that he called icosians, based on the symmetry properties
of the icosahedron. Hamilton connected the
mathematics of his icosians with the problem of traveling along the edges
of a dodecahedron, hitting each vertex just once, and coming back to the
starting point. His friend and fellow Irishman John Graves (1806–1870)
suggested turning the problem into a commercial game and put Hamilton in
contact with the London company of John Jacques and Sons, toy-makers and
manufacturer of high quality chess sets. Jacques bought the rights to the
game for £25 and marketed two versions of it, under the name Around the
World. One version, for the parlor, was played on a flat board; another,
for the "traveler," consisted of an actual dodecahedron. In both cases,
nails at each vertex stood for a major city of the world and the player
wrapped a piece of string around these nails as they went. In the event,
the game was a complete sales flop, mainly because it was too easy, even
for children – but not for Hamilton himself who always used the icosian
calculus to figure out his moves, instead of just trying different paths
like everyone else!